"Dear orthopedic doctors," please explain to me what science states that insoles and corsets are an effective treatment for posture problems?
The question is, of course, rhetorical. I know that in response I will hear some kind of incoherent mumbling, and the especially gifted will send me links to studies that they did not understand, or that were done crookedly. 
Let me take a moment to explain the harm of this "therapy." I'll start with the basics—how the peripheral nervous system controls muscles. That's physiology. What you missed or didn't understand in the medical textbook. 
So, there's the brain, the spinal cord, and the peripheral nerves. The brain decides to do something, for example, bend the arm. An action potential is generated in the brain—this is a nerve impulse that, like a relay race, is transmitted to the appropriate part of the spinal cord. From there, via motor neurons ( motor function) , the signal travels to the peripheral nerves of the arm (for example, the radial nerve). Once the action potential reaches the biceps, it contracts, BUT for the body to function properly, this is not enough.
There must be feedback to the brain; roughly speaking, to understand that the "bend the arm" command has been carried out by the right muscles, this requires sensory nerve function. Various mechanosensitive and other receptors receive information about muscle contraction, fascial tension, etc., and transmit this information back to the brain. The gist of it is this: if motor or sensory function is impaired, the brain doesn't receive enough information about the function of the relevant muscle and activates other muscles in the area to compensate for the muscle that failed to carry out its "order." I already wrote about this in a post about flat feet. For some reason, doctors still haven't figured this out.
Now, more practically, let me give you an example. What happens when using posture braces? Let's say our patient is slouched. They have some degree of kyphosis, scoliosis, or a spinal cord injury (due to a "pot-bottomed"/ online lifestyle). Some of their back muscles are stretched and don't contract (impaired motor function), while others are spasmodic (impaired sensory function) and don't relax properly.
This patient puts on a brace based on the recommendations of an "orthopedist." They tighten the straps, their shoulders recline, and they visually straighten up and go about their business, living their life. 
Everything will be relatively fine while they're wearing this brace. Problems will begin as soon as they take it off.
As someone has already guessed, from a biomechanical perspective, such a brace will be a poor artificial alternative to some of the patient's muscles. Moreover, these alternative "muscles" will be constantly contracted (due to the tight straps). But what will happen to the person's natural muscles?
Those muscles that were stretched and didn't contract will stretch even further, since the corset has taken over their function. Those that were in spasm will relax while wearing the corset, but will immediately spasm even more after you remove it. And I'm only briefly describing the negative aspects of this process; for example, I'm not going into the consequences for breathing, since the patient's diaphragm won't function properly while wearing the corset . The situation is similar with shoe insoles; I won't repeat myself; I described the details in my post about poor-quality footwear.
The end result is a patient who's sicker than they were before they went to the doctor. It's like immediately prescribing crutches to a person with gangrene. And you'll still have to pay for it.
In short, this kind of treatment should only be recommended to your enemies, to make them die faster.
